Is there any way of solving the following second-order ODE $$y''+\frac{(y'+2ay)^2+4b^2}{2y}+\frac{10}{3}a=0,$$ where $a$ and $b$ are some constant? If we know that one solution exists, how would it help to possibly find another solution?

Any help will be appreciated.

Is there any way of solving the following second-order ODE $$y''+\frac{(y'+2ax)^2+4b^2}{2y}+\frac{10}{3}a=0,$$ where $a$ and $b$ are some constant? If we know that one solution exists, how would it help to possibly find another solution?

Any help will be appreciated.

Is there any way of solving the following second-order ODE $$y''+\frac{(y'+2ay)^2+4b^2}{2y}+\frac{10}{3}a=0,$$ where $a$ and $b$ are some constant?

Any help will be appreciated.

Is there any way of solving the following second-order ODE $$y''+\frac{(y'+2ay)^2+4b^2}{2y}+\frac{10}{3}a=0,$$ where $a$ and $b$ are some constant? If we know that one solution exists, how would it help to possibly find another solution?

Any help will be appreciated.